发表机构
Tulane University; Imperial College London（杜兰大学; 伦敦帝国学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究二维随机Navier-Stokes方程上两类线性余圈对应的射影过程，通过局部渐近强耦合构造等方法证明其平稳测度唯一，解决了被动标量平流对应的非退化性证明难题。
AI 中文摘要
我们考虑由线性化涡度方程和被动标量平流扩散生成的线性余圈，两者均由二维环面上带非退化加性强迫的随机Navier-Stokes流驱动，我们证明了与这类线性动力学相关的射影过程的平稳测度的唯一性。该证明依赖于局部渐近强耦合构造，以及射影过程的Malliavin矩阵的非退化性。为被动标量平流建立这种非退化性带来了额外挑战，需要基于Cameron-Martin解析性论证证明：一般情形下被动标量处处非一维。
英文摘要
We consider the linear cocycles generated by the linearized vorticity equation and by passive scalar advection diffusion, both driven by the two dimensional stochastic Navier-Stokes flow on the torus with non degenerate additive forcing, and we prove uniqueness of the stationary measures for the projective process associated to such linear dynamics. The proof relies on a localized asymptotic strong coupling construction, and on the non-degeneracy of the Malliavin matrix of the projective process. Establishing this non-degeneracy for passive scalar advection poses additional challenges, and requires a proof (based on Cameron-Martin analyticity arguments) that generically the passive scalar is nowhere one-dimensional.
Comments77 pages, comments welcome
